2025 NJC P2 Q7

A toy train is made up of \(3\) types of train units: engine, carriage, and wagon. There are \(4\) identical engines \(\left( E \right)\), \(3\) identical carriages \(\left( C \right)\) and \(2\) identical wagons \(\left( W \right)\).

1. All the train units are placed in a line such that either the first unit is an engine or the last two units are engines, or both. Find the number of ways to form the toy train.[4]
2. For another kind of toy train, all the train units are placed in a line such that the first train unit is an engine and all the carriages are in front of the wagons. An example of such a toy train would be:
   \( E \ C \ C \ E \ E \ C \ W \ E \ W \).
   Find the number of ways to form the toy train.[3]